Macaulay2 » Documentation
Packages » CodingTheory » LinearCode » ambientSpace » BaseField
next | previous | forward | backward | up | index | toc

BaseField -- the field of a code

Description

Given a linear code C over a Galois field $F$, this symbol is used as a key for storing the Galois field $F$.

This symbol is provided by the package CodingTheory.

i1 : C = linearCode(GF(8,Variable => b), {{1,0,b,0,0},{0,b,b+1,1,0},{1,1,1,b,0}})

                                       5
o1 = LinearCode{AmbientModule => (GF 8)                                              }
                BaseField => GF 8
                cache => CacheTable{}
                Code => image | 1 0   1 |
                              | 0 b   1 |
                              | b b+1 1 |
                              | 0 1   b |
                              | 0 0   0 |
                GeneratorMatrix => | 1 0 b   0 0 |
                                   | 0 b b+1 1 0 |
                                   | 1 1 1   b 0 |
                Generators => {{1, 0, b, 0, 0}, {0, b, b + 1, 1, 0}, {1, 1, 1, b, 0}}
                ParityCheckMatrix => | 1 b2+1 b2+1 b2+1 0 |
                                     | 0 0    0    0    1 |
                                         2       2       2
                ParityCheckRows => {{1, b  + 1, b  + 1, b  + 1, 0}, {0, 0, 0, 0, 1}}

o1 : LinearCode
i2 : C.BaseField

o2 = GF 8

o2 : GaloisField

For the programmer

The object BaseField is a symbol.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/CodingTheory.m2:2868:0.